Risk estimates for toxic substances are based on the use of dose-response models to extrapolate high dose chronic quantal responses to low-dose environmental levels of human intake. Such estimates involve estimating the parameters of the models involved and then using such estimates to do low-dose extrapolation to an acceptable risk level yielding the virtual safe dose. We plan to do research on six different specific problems in this area: i) An extension to a model closely related to the multihit, multistage and Weibull models will be studied including parameter estimation, extrapolation procedures and comparison with existing models; ii) Statistical estimation and extrapolation procedures for some multivariate dose-response models will be studied; #iii) Certain dose-response models including the Weibull model will be extended to include a time-to-response factor in the hazard function. Estimation techniques using the notion of partial likelihood is envisioned; #iv) Certain dose-response models for estimation of teratological risk will be studied; #v) A method of incorporating the first order metabolic equation of Michaelis - Menten into existing dose-response models by estimation of an additional parameter to alter the administered dose to the "effective" metabolic dose; and #vi) Other problems including the incorporation of background response and nonstandard asymptotic theory to test for such response will be investigated.